The two sentences have the same meaning. They are both correct but the first feels more natural. The only difference is that the present participle, "watching", creates a feeling of ongoing activity whereas "I watch" merely states a fact. However, in this case there is no real reason to say "watching" because "working" already creates the feeling of ongoing activities. The use of both present participles in the same sentence feels redundant and less natural.

The difference between the two sentences lies in the use of verb tenses and the clarity of the statement. Let's break it down: "I am working on a presentation while I watch a movie." In this sentence, you are using the present continuous tense ("am working") to indicate an ongoing action. The second part of the sentence, "while I watch a movie," uses the simple present tense ("watch") to describe a simultaneous or habitual action. This combination suggests that you are currently in the process of working on a presentation while also watching a movie at the same time. "I am working on a presentation while I am watching a movie." In this sentence, you are still using the present continuous tense ("am working") for the first part. However, in the second part, "while I am watching a movie," you are also using the present continuous tense ("am watching") to emphasize that both actions are happening simultaneously. This adds a bit more detail and emphasis on the ongoing nature of both activities. In practical terms, the difference is subtle, and both sentences convey the idea that you are multitasking by working on a presentation and watching a movie at the same time. The choice between the two depends on your preference for tense consistency and the level of detail you want to convey.